As in, power-efficient? I'd suggest a 7850 or a GTX 660, in that case. They're both pretty power-efficient and do decently well at the resolution you're looking for. a 7850 1GB can be found for around... $180 on average, a 2GB for roughly $20 more, and a GTX 660 for maybe $220 or so. However, for about $210, you can also get an XFX Double D Radeon 7870 as well. Any of those cards, and especially the GTX 660 and the Radeon 7870, will work at the resolution you've got very well.
My HTPC acts as my backup gaming rig so if I were to buy a new video card for it just to get by until my gaming rig is fully operational again, then I would get the Radeon HD 7750.
The Radeon HD 7750 is relatively inexpensive at $99 maybe less if you can find one with a rebate. It is a mainstream card so that means you should be able to play most graphically demanding games at 1920x1080 resolution using medium graphic settings to get good (not excellent) frame rates / performance. It also uses very little power for the performance you get; peak power usage is 42w. You don't even need a power connection to the PSU. It is really power efficient and overall I like my HTPC to be as power efficient as possible while still having enough CPU processing power to do some video encoding.
For a little more money ($130) you can get the Radeon HD 7770 which is about 30% more powerful than the Radeon HD 7750 and it also consumes more power; 73w peak. It will need a connection to the PSU.
One last idea for you. If you have some time, why don't you look at a 1GB version of the HD 5670 DDR5? It's a great card and would fit nicely with your requirements, and I suspect you could find it very cheap. I have one, and it's perfect for my casual gaming requirements.